Completeness

Revisiting Russell on Cause

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We discussed Bertrand Russell’s criticism of the first cause argument here. As I said there, he actually suggests, although without specifically making the claim, that there is no such thing as a cause, when he says:

That argument, I suppose, does not carry very much weight nowadays, because, in the first place, cause is not quite what it used to be. The philosophers and the men of science have got going on cause, and it has not anything like the vitality it used to have.

This is absurd, and it is especially objectionable that he employs this method of insinuation instead of attempting to make an argument. Nonetheless, let me attempt to argue on Russell’s behalf for a moment. It is perhaps not necessary for him to say that there is no such thing as a cause. Suppose he accepts my account of cause as an explanatory origin. Note that this is not purely an objective relationship existing in the world. It includes a specific relationship with our mind: we call something a cause when it is not only an origin, but it also explains something to us. The relatively “objective” relationship is simply that of origin.

A series of causes, since it is also a series of explanations, absolutely must have a first, since otherwise all explanatory force will be removed. But suppose Russell responds: it does not matter. Sure, this is how explanations work. But there is nothing to prevent the world from working differently. It may be that origins, namely the relationship on the objective side, do consist of infinite series. This might make it impossible to explain the world, but that would just be too bad, wouldn’t it? We already know that people have all sorts of desires for knowledge that cannot be satisfied. A complete account of the world is impossible in principle, and even in practice we can only obtain relatively local knowledge, leaving us ignorant of remote things. So you might feel a need of a first cause to make the world intelligible, Russell might say, but that is no proof at all that there is any series of origins with a first. For example, consider material causes. Large bodies are made of atoms, and atoms of smaller particles, namely electrons, protons, and neutrons. These smaller particles are made of yet smaller particles called quarks. There is no proof that this process does not go on forever. Indeed, the series would cease to explain anything if it did, but so what? Reality does not have to explain itself to you.

In response, consider the two following theories of water:

First theory: water is made of hydrogen and oxygen.

Second theory: every body of water has two parts, which we can call the first part and the second part. Each of the parts themselves has two parts, which we can call the first part of the first part, the second part of the first part, the first part of the second part, and the second part of the second part. This goes on ad infinitum.

Are these theories true? I presume the reader accepts the first theory. What about the second? We are probably inclined to say something like, “What does this mean, exactly?” But the very fact that the second theory is extremely vague means that we can probably come up with some interpretation that will make it true, depending in its details on the details of reality. Nonetheless, it is a clearly useless theory. And it is useless precisely because it cannot explain anything. There is no “causality” in the second theory, not even material causality. There is an infinite series of origins, but no explanation, and so no causes.

The first theory, on the other hand, is thought to be explanatory, and to provide material causes, because we implicitly suppose that we cannot go on forever in a similar way. It may be that hydrogen and oxygen are made up of other things: but we assume that this will not go on forever, at least with similar sorts of division.

But what if it does? It is true, in fact, that if it turns out that one can continue to break down particles into additional particles in a relatively similar manner ad infinitum, then “water is made of hydrogen and oxygen” will lose all explanatory force, and will not truly be a causal account, even in terms of material causes, even if the statement itself remains true. It would not follow, however, that causal accounts are impossible. It would simply follow that we chose the wrong account, just as one would be choosing wrongly if one attempted to explain water with the second theory above. The truth of the second theory is irrelevant; it is wrong as an explanation even if it is true.

As I have argued in a number of places, nature is not in the business of counting things. But it necessarily follows from this that it also does not call things finite or infinite; we are the ones who do that. So if you break down the world in such a way that origins are infinite, you will not be able to understand the world. That is not the world’s problem, but your problem. You can fix that by breaking down the world in such a way that origins are finite.

Perhaps Russell will continue to object. How do you know that there is any possible breakdown of the world which makes origins finite? But this objection implies the fully skeptical claim that nothing can be understood, or at least that it may turn out that nothing can be understood. As I have said elsewhere, this particular kind of skeptical claim implies a contradiction, since it implies that the same thing is known and unknown. This is the case even if you say “it might be that way,” since you must understand what you are saying when you say it might be that way.

Self Reference Paradox Summarized

entirelyuseless Logic, Mathematics, Metaphysics, Uncategorized , , , , , , , , , , , , , , ,

Hilary Lawson is right to connect the issue of the completeness and consistency of truth with paradoxes of self-reference.

As a kind of summary, consider this story:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:

It was a dark and stormy night,
and all the Cub Scouts where huddled around their campfire.
One scout looked up to the Scout Master and said:
“Tell us a story.”
And the story went like this:
etc.

In this form, the story obviously exists, but in its implied form, the story cannot be told, because for the story to be “told” is for it to be completed, and it is impossible for it be completed, since it will not be complete until it contains itself, and this cannot happen.

Consider a similar example. You sit in a room at a desk, and decide to draw a picture of the room. You draw the walls. Then you draw yourself and your desk. But then you realize, “there is also a picture in the room. I need to draw the picture.” You draw the picture itself as a tiny image within the image of your desktop, and add tiny details: the walls of the room, your desk and yourself.

Of course, you then realize that your artwork can never be complete, in exactly the same way that the story above cannot be complete.

There is essentially the same problem in these situations as in all the situations we have described which involve self-reference: the paradox of the liar, the liar game, the impossibility of detailed future prediction, the list of all true statements, Gödel’s theorem, and so on.

In two of the above posts, namely on future prediction and Gödel’s theorem, there are discussions of James Chastek’s attempts to use the issue of self-reference to prove that the human mind is not a “mechanism.” I noted in those places that such supposed proofs fail, and at this point it is easy to see that they will fail in general, if they depend on such reasoning. What is possible or impossible here has nothing to do with such things, and everything to do with self-reference. You cannot have a mirror and a camera so perfect that you can get an actually infinite series of images by taking a picture of the mirror with the camera, but there is nothing about such a situation that could not be captured by an image outside the situation, just as a man outside the room could draw everything in the room, including the picture and its details. This does not show that a man outside the room has a superior drawing ability compared with the man in the room. The ability of someone else to say whether the third statement in the liar game is true or false does not prove that the other person does not have a “merely human” mind (analogous to a mere mechanism), despite the fact that you yourself cannot say whether it is true or false.

There is a grain of truth in Chastek’s argument, however. It does follow that if someone says that reality as a whole is a formal system, and adds that we can know what that system is, their position would be absurd, since if we knew such a system we could indeed derive a specific arithmetical truth, namely one that we could state in detail, which would be unprovable from the system, namely from reality, but nonetheless proved to be true by us. And this is logically impossible, since we are a part of reality.

At this point one might be tempted to say, “At this point we have fully understood the situation. So all of these paradoxes and so on don’t prevent us from understanding reality perfectly, even if that was the original appearance.”

But this is similar to one of two things.

First, a man can stand outside the room and draw a picture of everything in it, including the picture, and say, “Behold. A picture of the room and everything in it.” Yes, as long as you are not in the room. But if the room is all of reality, you cannot get outside it, and so you cannot draw such a picture.

Second, the man in the room can draw the room, the desk and himself, and draw a smudge on the center of the picture of the desk, and say, “Behold. A smudged drawing of the room and everything in it, including the drawing.” But one only imagines a picture of the drawing underneath the smudge: there is actually no such drawing in the picture of the room, nor can there be.

In the same way, we can fully understand some local situation, from outside that situation, or we can have a smudged understanding of the whole situation, but there cannot be any detailed understanding of the whole situation underneath the smudge.

I noted that I disagreed with Lawson’s attempt to resolve the question of truth. I did not go into detail, and I will not, as the book is very long and an adequate discussion would be much longer than I am willing to attempt, at least at this time, but I will give some general remarks. He sees, correctly, that there are problems both with saying that “truth exists” and that “truth does not exist,” taken according to the usual concept of truth, but in the end his position amounts to saying that the denial of truth is truer than the affirmation of truth. This seems absurd, and it is, but not quite so much as appears, because he does recognize the incoherence and makes an attempt to get around it. The way of thinking is something like this: we need to avoid the concept of truth. But this means we also need to avoid the concept of asserting something, because if you assert something, you are saying that it is true. So he needs to say, “assertion does not exist,” but without asserting it. Consequently he comes up with the concept of “closure,” which is meant to replace the concept of asserting, and “asserts” things in the new sense. This sense is not intended to assert anything at all in the usual sense. In fact, he concludes that language does not refer to the world at all.

Apart from the evident absurdity, exacerbated by my own realist description of his position, we can see from the general account of self-reference why this is the wrong answer. The man in the room might start out wanting to draw a picture of the room and everything in it, and then come to realize that this project is impossible, at least for someone in his situation. But suppose he concludes: “After all, there is no such thing as a picture. I thought pictures were possible, but they are not. There are just marks on paper.” The conclusion is obviously wrong. The fact that pictures are things themselves does prevent pictures from being exhaustive pictures of themselves, but it does not prevent them from being pictures in general. And in the same way, the fact that we are part of reality prevents us from having an exhaustive understanding of reality, but it does not prevent us from understanding in general.

There is one last temptation in addition to the two ways discussed above of saying that there can be an exhaustive drawing of the room and the picture. The room itself and everything in it, is itself an exhaustive representation of itself and everything in it, someone might say. Apart from being an abuse of the word “representation,” I think this is delusional, but this a story for another time.